External Reorganization Energy upon Charge Transfer Reactions in Mildly Polar Media: The Case of Naphthalene in Tetrahydrofuran.

External reorganization energy, λ, is of paramount importance in condensed-phase electron transfer (ET) processes, but its precise determination remains a challenge. We here combine classical molecular dynamics with advanced electronic-structure calculations and the thermodynamic integration technique to calculate λ for a mildly polar solvent, tetrahydrofuran (THF), in ET reactions involving the (NAP/NAP) redox couple (NAP = naphthalene), a system widely studied in this context. First, we simulate the structural and electronic properties of liquid THF, as well as those of NAP and NAP solutions, in excellent agreement with available measurements. Then, from the calculated vertical and adiabatic energy levels, we determine the values of λ associated with the reduction of NAP and the oxidation of NAP. We observe a clear asymmetry in the solvent response for the two processes, which could not be captured by either the Marcus approximation or using standard implicit solvent models. Finally, we identify the different contributions to λ that are at the root of nonlinear solvent response, including dipole-charge interactions and effects arising from induced polarization. These interactions are found to be most significant in the first solvation shell, particularly for a limited number of solvent molecules closest to the solute.